Don’t Think of a Square Circle!

Don’t Think of a Square Circle!

Wittgensteinian Reflections on Imagining the Impossible

3.031 It used to be said that God could create anything except what would be contrary to the laws of logic. The truth is that we could not say what an 'illogical' world would look like. 

—Wittgenstein, Tractatus Logico-Philosophicus, trans. D. F. Pears and B. F. McGuinness (London: Routledge & Kegan Paul)

Available at: http://www.voidspace.org.uk/psychology/wittgenstein/tractatus.shtml

It has been noted (by George Lakoff, among others) that if someone tells you “Don’t think of an elephant!”, it’s pretty hard not to do it. Though it would take empirical research to fill in the details, the answer as to why this is so does not seem hard to discern: To understand the order—to understand what one is not supposed to think of—one must understand the term ‘elephant’, and thus come to think of one. I’d wager that in addition to thinking of one an image of an elephant popped into your head as well. This is probably because the concept of an elephant is an empirical concept—no crisp, abstract definition of an elephant comes readily to mind, so a stereotypical image is needed to make it intelligible. By contrast, if someone were to tell you “Don’t think of the number 2!” it is less likely that an image would come up, unless you confuse the numeral ‘2’ with the number 2—or, at least, that the image would be unlikely to be constant for different people, or for the same person at different times.

What, though, if someone were to tell you “Don’t think of a square circle!” Is it so hard to comply in this case?

Well, maybe it is: Do I really know what it is I’m not supposed to think of? If not, I’m not really complying with the order, because I fail to understand it. I’m merely doing what it says. Nevertheless, what interests me here is not our concept of compliance, but rather that of conceiving or imagining the impossible.

If one can imagine or conceive of something, what then could one mean by saying that one can’t understand how it could be the case? Could it be, for instance, that I can conceive that a square circle exists, but not that the existence of a square circle is possible? It would seem not: It is not more impossible that it is possible that a square circle exists than that a square circle exists; so if I can conceive the latter, I should be able to conceive the former as well. If however, I cannot conceive of the existence of a square circle, I cannot conceive of its possibility either. That seems fine, but one could ask: If I cannot conceive of a square circle, nor of its possibility, how could I still conceive of its impossibility? That is, if I truly cannot conceive of it, how can I say that it is that, and not something else, or nothing at all, of which I am unable to conceive? If someone tells me that I cannot eat or drink on the subway, I know what it is that I am being forbidden to do. And if I am informed that no human being can run as fast as a cheetah, I know what is being declared to be impossible, and it is relatively easy to form an image of what the contrary would look like. But if someone tells me that it is impossible for a circle to be square, or identical to (i.e., the same thing as) a square, how am I to know what it is that is being said to not possibly be the case?  For if you were to be told that snorogs are impossible, you would have every right to ask your alleged informant what a snorog is. If no answer were forthcoming, the most you could conclude is that you cannot know whether they are possible or not if you have no idea what they are supposed to be. The same should hold just as much for “square circles”: If I simply don’t know what the term means I should conclude, not that they cannot exist, but rather that I have no idea whether they can or not, if the term is meaningful at all. And if I do understand it, it seems—as was said above—that I must also be able to understand the claim that square circles are possible, as the possibility of something cannot be any more impossible than the thing itself. If I nevertheless say that they or their possible existence is inconceivable, I cannot mean that I do not understand the claim that they exist, or that their existence is possible. What, then, can I mean? 

A natural answer would be something like: In virtue of understanding the term ‘square circle’, I “see” or “grasp” that they cannot exist. But what am I seeing here, and how do I see it?

The second question would involve us in the thorny details of epistemological debates surrounding a priori knowledge, which I will not enter into. By contrast, it might seem that an answer to the first question is trivial: I’m seeing that square circles cannot exist! But what we have said so far should make us suspicious of this answer. To be sure, it is a right answer to our question, if it’s true that I’m really seeing that, but it’s not the only possible answer, and certainly not the most helpful one. If someone were to tell you that they can see that snorogs cannot exist, and you were to ask them what exactly it is to see that, it would not be very informative to be told that it is simply to see that snorogs cannot exist! If you don’t know yourself what snorogs are, or what ‘cannot’ means in this context, such an answer won’t help you one bit. We have two problems: (1) If I am to “see that something cannot be the case” in virtue of understanding a term, ‘cannot’ should not mean: It is inconceivable that it is the case. What, then, does it mean? It must be more than mere nomic or physical impossibility, for one cannot tell something to be nomically or physically impossible merely in virtue of understanding a certain term. (2) How am I to tell whether I or someone else truly understands the term? For unless I have some means of doing so I am at a loss as to how to assess the claim of impossibility, and can make no progress.

I’ll leave the first question to one side (for now). As for the second, in all cases it should be possible to specify the meaning of a term somehow, to give some kind (not necessarily very exact and not necessarily very informative) of explanation or definition of what it is. In addition, for empirical terms it should be possible to imagine the corresponding entity or recognize it in experience.

Can one specify the meaning of ‘square circle’? It certainly seems so: One can define it as a circle that is also a square, or as a circle that is identical to (is the same thing as) a square. Alternatively, if the term ‘spherical cube’ is already understood, (as, e.g., a sphere that is also a cube, or a sphere that is identical to a cube) one could define a square circle as a 2-dimensional cross-section of a spherical cube that cuts through its center. Admittedly, these definitions are not very rigorous, but rigorous definitions cannot be given for most terms in ordinary use, and they are none the worse off for that.

One can note that as ‘square’ and ‘circle’ (or ‘sphere’ and ‘cube’) are empirical terms, ‘square circle’ should  be one too. But whereas it has appeared easy to define what a square circle would be, it seems much more difficult to imagine what one would look like. Supposing one were shown a drawing of a disc with a large square hole in it, or a square solid with a large circular hole in it, one would naturally reply that that isn’t what one means . But what then does one mean? It is not as though I have some (vague) image of a square circle to which they fail to conform, but rather that no image suggests itself. Is it that it would look like something, only I don’t know what? Or is it that there is no such thing as “what it would look like”?

Well, if the One True Logic is not paraconsistent (i.e., is not non-explosive), then contradictions entail everything. So if square circles are contradictory—and they seem to be, for squares are square and circles are not, while square circles are both squares and circles—then every counterfactual beginning “If there were square circles, they would look like…” is true. If Logic is not paraconsistent, then, nothing is easier than imaging what a square circle would look like: Take anything you please, such as a shoe, a ship, some sealing wax, a cabbage, or a king. If the One True Logic is paraconsistent, matters are less clear. But suppose some lover of paradoxes were to come to you, draw a square and a circle next to each other, and ask you whether a square circle would look like that.

“Like the square or the circle?”, you enquire.

“Like both,” he replies.

“Well,” you say, “a square circle is supposed to be a square that’s identical to a circle, but the figures you have drawn don’t look identical.”

“I grant that the figures I have drawn are not identical,” he replies, “but that’s the thing about representations: they need not share the properties of the things they represent. As for identity, I wasn’t aware that it looked like anything at all. If it did, one could tell by mere inspection whether properties are universals or tropes, by ostending different “instances” or “tokens” of the same type and checking to see—literally see—that the instances either do or do not have something numerically identical in common; and one could thus very easily settle that dispute. As things are this is not possible, so it seems safe to say we cannot perceptually experience relations of identity. So I think I can safely say that the circle and the square are depicted as being identical, even though the depicted square and the depicted circle don’t look identical.

“Identity may not look like anything,” you reply, “but difference certainly does, and the square depicted and the circle depicted look different.

“Naturally,” he replies, “for I have drawn a contradictory object, which is naturally both self identical and self-distinct. Since I have drawn a square which is identical to a circle, it differs even from itself, and it is this difference which you are picking up on.”

“Well,” you say, more hesitantly, “not only do they look different, they appear to be in different places. A square circle isn’t supposed to be a mereological sum of a square in one place and a circle in another, but one thing in one place which is both square and circular.”

“That,” he replies, “is merely a defect of the medium. I drew a square shape and a circular shape in different places, but they are intended to depict exactly the same location. And in any case, just as the depicted shape is both self-identical and self-distinct, the depicted location of the shape must also be both self-identical and self-distinct. The places of the shape(s) are thus both different and not different, and again it is the difference which you are picking up on.”

“But,” you sputter in exasperation, “I can see that the square and the circle are different from each other, and also that they are not different from themselves, but what I cannot see is that they are not different from each other!”

“But of course you can!” he replies, smiling, “for take the depicted square. You can surely see that it is not different from itself; that is, that the square is not different from the square. And since that square is identical to the depicted circle, it follows by Leibniz’s Law that the depicted circle looks not to be different from the depicted square!”

At this point I suspect you would give up, and let the lover of paradoxes go on his merry way. But who has won the hypothetical dispute? Why shouldn’t we say that his drawing of a square circle is a perfectly good one—that by looking at it we can now tell what one would look like? If we still insist, as I think most will, that his drawing isn’t a good one, I think the proper moral may well be a Wittgensteinian one: When we say that we cannot imagine a square circle, what we’re really doing (whether we realize it or not) is excluding any purported description of what one would look like from our language-game(s). We’re saying, in effect, “No matter what anything looks like, we refuse to call that ‘what a square circle looks like’, and no matter what anyone draws, we refuse to call it ‘a good drawing of a square circle.’ And this isn’t to say that there can’t be some strange looking drawings—one can simply look at a Penrose triangle or some of M.C. Escher’s works (or for a real life case, one can check out ‘the waterfall illusion’). One must get away from the idea that behind a grammatical rule there stands something that cannot be done—unless one only means that there is a norm that we shouldn’t speak in a certain way. Any image can be described in language in multiple ways, and what the case of the lover of paradoxes shows, if it shows anything, is that our current, actual language game forbids certain descriptions of certain phenomena. Perhaps, as in the case of the waterfall illusion, a language game which admits of inconsistent modes of description would be more appropriate (and note that I say more appropriate, for consistent modes of description are certainly also available). As with the description ‘the pitch of sweetness’, the (apparent) description ‘the look / appearance of a square circle’ has been denied a role in our language game. Just as ‘the pitch of sweetness’ is not something we fail to hear in any ordinary sense, ‘the look / appearance of a square circle’ is not something that we fail to see or imagine in any ordinary sense. Why such terms play no role in our language may be hard to say, but that they do not could be said to be shown by our reaction to the case of the lover of paradoxes: the simple fact is that we know how the investigation is to turn out before we begin to inquire. For it is not that the term ‘square circle’, like the term ‘snorog,’ simply calls up no image for us as a matter of fact—if someone were to introduce us to a community where things which were regularly called snorogs looked such-and-such a way, we would accept that easily—it is rather that we know in advance that we will refuse to apply the term ‘square circle’ to anything.

In this way we avoid the misleading idea of imagining the impossible as something that we are unable to do—that “our powers of imagination are unequal to the task” as Wittgenstein put it in the Investigations—as well as avoiding the equally misleading picture of logical or conceptual necessity whereby we in effect personify it as the bouncer at the door of Club Reality; of logical/conceptual necessity as a powerful force which keeps out the riffraff of impossibilia struggling to get in in order that they may exist. This, at any rate, is the best I think I can do to give content to Wittgenstein’s idea of logical/conceptual necessity as being basically linguistic.

Philosophy Limerick of the Day: Wittgenstein

There was once a philosopher, Witt
Who acted just like a git
He picked up a poker, and when thought a joker
Stormed out of the room in a fit

Philosophy of Language Notes Part 1: Wittgenstein

Over at Scholardarity I've posted Part 1 of my notes on the Philosophy of language, the first contribution to Scholardarity Student’s subsection Open Source Study Notes. This  part deals with the philosophy of Ludwig Wittgenstein. Here's an excerpt:

~ Prelude ~

Why philosophers study language–

1) Philosophers have been accused of “making mistakes” based on language. Consider the sentences:

i) “Santa Claus does not exist.”

ii) “Santa Claus wears a red suit.”

a) “How can one talk about something”, philosophers sometimes ask, “and say something true or false about it, if it isn’t real or doesn’t ‘have being’ in some sense? In order for statements like (i) or (ii) to be true, they have to be about something—Santa Claus, in this case. Granted, in light of the fact that (i) is true, Santa Claus doesn’t exist, but nevertheless he is some kind of being and has properties—including the properties of being non-existent and wearing a red suit.” However, at least since Bertrand Russell published his famous article “On Denoting” in 1905, most philosophers think that arguments like this are based on linguistic confusions. It can be true that Santa Claus does not exist without Santa Clause being real in any sense.

b) From time to time philosophers also ask: Is there such a thing as “goodness”, or something like Plato’s “Form of the Good”? Able philosophers have thought so, but others–emotivists, in particular, such as A. J. Ayer, C. L. Stevenson, Richard Hare—have held that to call something good or bad, or to say that an action is right or wrong, is not to say that it objectively has some moral feature—“goodness”, “wrongness”, etc.—but to express how the speaker feels about the thing or action in question.  For example, on this view a sentence like “Lying is wrong” is neither true nor false; nor, when properly understood, is it purported to be. It merely evinces that the speaker who uttered the sentence disapproves of lying. It does not even say that the speaker disapproves of lying—that would be a sentence that is apt to be true or false; true if the speaker disapproves of lying and false if they do not. On the emotivists’ view, to say that lying is wrong is more like saying “Boo lying!”, “Screw lying!”, “Down with lying!”, or something of the sort.

(Personal note: Words like ‘good’ and ‘bad’, ‘right’ and ‘wrong’, may have an expressive function, but it doesn’t follow that they only have an expressive function. Sentences involving ‘good’ and ‘bad’ might sometimes attribute objective goodness or badness to some entity, and it may be that it is in virtue of one’s belief that the entity in question is objectively good that one can use the term ‘good’ or ‘goodness’ to express how one feels about it. For it may be that if one had no belief concerning the entity’s moral value, one might not have any feelings about it, whether positive or negative.)

2) What are the limits of human knowledge? What can we conceive? The “early” Ludwig Wittgenstein, for example, thought there was a connection between the limits of conception and the limits of what can be expressed in language:

The book will, therefore, draw a limit to thinking, or rather—not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought).

The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense.—Tractatus Logico-Philosophicus, p. 3

3) Language is inherently interesting.

John Searle's Chinese Room Argument

Check out my YouTube video critiquing John Searle's Chinese Room Argument, as read by Philosobot: 

http://www.youtube.com/watch?v=lhKlqfkIoB0


Live long and philosophize!

Against Hacker on the Justifiability of Grammar

Over at Methods of Projection, in the comments section of a post about Wittgenstein on meaningfulness and language games, N. N. posted the following arguments by P. M. S. Hacker, which attempt to show that the rules of grammar cannot be justified:

Justifying grammar by reference to the facts leads to an infinite regress. Any attempt to justify grammatical rules by reference to how things are in reality must employ a language in giving that justification. The form of words that purports to justify a rule of grammar must itself have a grammar. If it has the same grammar as that which it purports to justify, the justification begs the question. If it has a different grammar, then (a) it determines different concepts and so cannot be about the same thing, hence is irrelevant; and (b) that grammar too will stand in need of justification. So any attempt at grounding grammar is reality will launch us upon an infinite regress of justifications.
[...]
No description of reality can justify grammar. Any attempt to justify grammar by reference to reality must take the form of a grammatically licit description of how things are. Such a description is given by a proposition with a sense. Consequently its negation too must make sense, for the negation of a proposition with sense, which describes how things are, is itself a proposition with sense. But for such a proposition to justify a grammatical rule which delimits the sense of sentences and excludes nonsensical forms of words, the negation of the justifying description would have to be nonsense, not a falsehood. This has two corollaries, both of which were discussed by Wittgenstein.
(a) If it were possible to justify grammatical rules by reference to reality, those rules would be superfluous. One cannot say that a grammatical rule is made necessary by certain properties of things: e.g. the rule that excludes the words 'transparent white' or 'flashing black' cannot be justified by saying that white is not transparent or that black is not radiant. For if one could say this, then it would make sense, even though it would be false, to say that this white glass is transparent or that the traffic lights flashed black. But then the grammatical rule would be superfluous, since what it does is precisely to exclude such forms of words as nonsense.
(b) Any justification of grammar by reference to reality requires the possibility of describing a reality that would not justifify that grammar. A justifcation of our grammar by reference to reality should, it seems, take the form of saying that since reality is thus-and-so, the rules of grammar must be such-and-such. But one must then also be able to say that if reality were otherwise, then the rules of grammar would have to be different. However, one cannot sensibly say how reality would have to be in order for a different grammar to be justified. For in order to describe such a different reality, one would have to use the very combinations of words which our existing grammar excludes, i.e. one would have to talk nonsense. But if something counts as nonsense in the grammar which is to be justified, it cannot at the same time pass for sense in the grammar of the propositions purporting to justify it.

To this I responded as follows:

Hi n.n.,

I disagree with Hacker's arguments for the unjustifiability of grammar for the following reasons: First, it seems to me his regress argument works, if it works at all, only if we take sentences as the ultimate bearers of truth. If one believes in abstract propositions, as I'm inclined to do, one can hold that the justifications one gives for the grammar of some language, being abstract propositions which may be expressed in several languages each with a different grammar, don't have a grammar in the required sense. I'm sure Hacker would reject the existence of such propositions, but he would need to give some independent argument for doing so. Second, and more importantly, it seems to me that his arguments about nonsensicality vs. falsehood are self-referentially incoherent. Let us take, for example, the statement "No description of reality can justify grammar." Hacker takes this to be true. If it is true it certainly makes sense, but if it makes sense then (according to Hacker) so must its negation, namely "Some description of reality can justify grammar"; and if it makes sense Hacker can't rule it out a priori. On the other hand, if "Some description of reality can justify grammar" is nonsense, then (by Hacker's lights) so is the statement "No description of reality can justify grammar." Thus it appears that the conclusion Hacker wishes to establish is either false or nonsensical. Where does that leave us? One might think these considerations show that there are some statements which are meaningful but necessarily false. Personally, I think this is probably the correct conclusion. But there's another option which is often overlooked-- one could say that some meaningful statements simply don't have a meaningful negation at all.

The rest of the discussion is also quite interesting, so if you have the time by all means go check it out.

In Defense of Private Language: Part 2

Kripke’s theory of naming—though he refuses to call it that—is a reaction against the views of Gottlob Frege and Bertrand Russell. They had thought that the reference of a name is determined by a description which is associated with it in the mind of a speaker. Thus the reference of a name such as 'Aristotle' may be determined by a description such as “the most famous student of Plato.” Kripke makes several criticisms of this kind of account of names, which I cannot go into here. The important thing is the positive view that Kripke develops in response to it.

If the Frege-Russell view is wrong, how does it come about that people are able to use names to refer to objects? On Kripke’s theory, names are simply labels that we tag objects with. They can pick out their referents directly, without a need for any mediating description. In place of a description, Kripke envisions a causal chain stretching from current utterances of a given name all the way back to an initial “baptism” of its bearer. (Naming and Necessity, pp. 96-97) During a typical baptism a person will attend or point to an object which causally affects them in some way—perhaps by the light it reflects—and pronounce a word which, in the right circumstances[1], becomes the object’s name. Others hear the baptizer utter this name and come to use it themselves. Still others hear it from them and come to use it as well, etc. In this way the name can be passed on to an ever increasing number of speakers. So long as they intend to use the name to refer to the same thing the original baptizer used it to refer to, they too can use it to refer to that thing, even if they have never encountered it and know next to nothing about it. Indeed, they can successfully use the name to refer to it when most of their beliefs about it are false. These results are a great strength of Kripke’s theory, and one would do well to remember them, for they are crucial to understanding how the Private Language Argument goes wrong.

If Kripke’s account of naming is correct, we may say either that names refer but have no meaning, or that the meaning of a name just is its bearer. Either way, Wittgenstein’s view is in trouble, for the Private Language Argument rests on the assumption that names do have a kind of meaning, in the form of a rule which governs their correct application. Consider this excerpt from section 258 of PI : “A definition surely serves to establish the meaning of a sign.—Well, that is done precisely by the concentrating of my attention; for in this way I impress on myself the connexion between the sign and the sensation.—But “I impress it on myself” can only mean: this process brings it about that I remember the connexion right in the future. But in the present case I have no criterion of correctness.” (PI p. 92) But it is doubtful that such a conception of meaning applies to the sort of expressions being considered here. What, for instance, would the rule for the correct use of the name ‘Aristotle’ be? Would it be “Apply the name ‘Aristotle’ to Aristotle and nothing else”? If one does not already “understand” the name ‘Aristotle’ this rule is useless, and if one does understand it the rule is entirely superfluous. Note also how Wittgenstein quickly passes from saying that a definition[2] establishes the meaning of a sign to saying that one impresses a connection on oneself through an act of attention. The connection between a sign and a sensation is a relation of reference, and if one thinks of reference as Kripke does it will sound very odd to talk of “impressing” such a relation on oneself or of “remembering” it. What could it mean, on a view like Kripke’s, to impress on oneself the connection between the name ‘Aristotle’ and the man to whom it refers? For Kripke this connection is constituted by a certain series of causal relations, and it exists whether I remember it or not.

The truth is that, to use the name ‘Aristotle’ meaningfully—or “referentially,” if we hold names to be meaningless—one need only stand in certain causal relations to Aristotle and intend to use the name to refer to the same thing as those from whom one got it. Whether one also has certain beliefs about Aristotle, undertakes to “use” the name ‘Aristotle’ in a certain way, or is able to “remember” the referential link between the name and its bearer will not affect the meaning or reference of the name. Apart from this there is no criterion for its correct use. Names can be used significantly because they stand in certain relations to something in the world, not because of any rules we supply to govern their application. The same, I contend, goes for the terms of a private language.

In opposition to Wittgenstein, I propose the following Kripke-inspired picture of the meaningfulness of sensation words. Suppose I am a private linguist who wants to record occurrences of a private sensation—a toothache, for instance—in a calendar of the sort Wittgenstein mentions in section 258 of PI. On having the toothache I go over to the calendar and inscribe the sign ‘T’. Since I am trying to keep track of the recurrence of this sensation, I am evidently using ‘T’ a general term, not as a name for that particular toothache. The term ‘T’ is, when used in this way, a natural kind term. To establish its reference I simply attend to my toothache and think something like “Let this kind of pain be called ‘T’,” just as I can attend to a particular kind of substance and say “Let this kind of metal be called ‘gold’.” In order to establish a relation between my sign ‘T’ and this kind of pain I need not impress on myself any connection or give myself any rule for its use, for terms which are introduced in this way either have their referent as their meaning or have no meaning at all. The baptism itself is all that is needed for me to use the sign significantly. Once the reference of ‘T’ has been established, I can use the sign in the future to refer to the same class of pains simply by intending to use it in the same way I originally did, even if the initial baptism has long since been forgotten and I now apply the term ‘T’ (incorrectly) to pains which are not toothaches. The reference is passed on to my future selves much as the reference of proper names such as ‘Aristotle’ is passed on to subsequent speakers. Moreover, if others should stumble across my calendar they can also use the sign ‘T’ to refer to my toothaches, even if they have no means of discovering what ‘T’ stands for.

We have seen that if the Private Language Argument is sound, sensation words must have publicly accessible criteria for their correct application in order to be meaningful. If there is no such thing as a criterion for the correct use of words of this kind, Wittgenstein’s argument falls apart. The upshot of the foregoing considerations is that if Kripke’s theory of naming is right the notion of a private language may be intelligible after all, in which case it is Wittgenstein himself who has fallen victim to a conceptual confusion.

Bibliography

Kripke, Saul A. Naming and Necessity. Cambridge, Massachussetts: Harvard University Press, 1980.

Wittgenstein, Ludwig. Philosophical Investigations, 3^rd Edition. Trans. G.E.M.

Anscombe. Engelwood Cliffs, New Jersey: Prentice Hall, 1958.

---

[1] These circumstances may include such background conditions as that the object does not already have a name or that the baptizer is authorized to name this object.

[2] By which he means ostensive definition, as is made clear earlier in section 258.

In Defense of Private Language: Part 1

(The following is my final paper for the Philosophy of Language course I took last semester, lightly edited to improve grammar and clarity. I've also divided it into two parts so you don't have to read the whole thing in one sitting.)

Wittgenstein’s Philosophical Investigations (henceforth PI) is a deep and important book, densely packed with thought experiments and many insightful observations. One of the most significant themes running through this work can be found in a chain of related aphorisms containing Wittgenstein’s ruminations on the possibility of a private language—a language whose terms are intelligible only to its speaker. Collectively known as the Private Language Argument, they are designed to show that the notion of a private language is incoherent. This argument, if sound, would be of lasting significance to philosophy, for it has the potential to overthrow some deep-seated intuitions about the mind. In what follows I shall attempt to show that, even if such a language is impossible, the Private Language Argument does not give us a good reason for thinking it is.

The main thrust of Wittgenstein’s arguments concerning the possibility of a private language seems to be that a would-be private linguist has no means of telling whether they are using a sign which purportedly picks out one of their private sensations correctly or not. For a private linguist to use a sign for one of their sensations meaningfully there must be a distinction between correct and incorrect usage. But what could this distinction consist in for a term of a private language? Not in its agreement or disagreement with how the term is used by others in the private linguist’s community, for by hypothesis the meaning of the term is not determined by and cannot be inferred from anything that is publicly observable, including the private linguist’s behavior. Nor can its correctness consist in its conformity with the private linguist’s judgments regarding whether they are having the same sensation or a different one, for then the distinction between correct and incorrect usage would evaporate. For what we are after here are not merely the conditions under which, as a matter of fact, the term is correctly or incorrectly used, but rather what it is for the term to be used correctly or incorrectly. The issue at stake in the Private Language Argument is not the skeptical one of whether, given that there are private sensations, we can be sure that for the most part we are applying our sensation words to them correctly. The issue is instead whether talk of such things as private sensations is meaningful at all. So when Wittgenstein demands criteria for the correct use of words, what he wants is simply some means of distinguishing correct from incorrect use; how often our use is correct is immaterial. Now, if the criterion for the correct use of a term in a private language is its accordance with the judgments of the private linguist, it will be nonsense to speak of any possibility of error. As Wittgenstein puts it, “One would like to say: whatever is going to seem right to me is right. And that only means that here we can’t talk about ‘right’.” (Section 258; PI. p. 92) Yet if the correct or incorrect application of the term is established neither by public use nor private judgment, what else could establish it? I think there is another possibility, but we must critically examine Wittgenstein’s account of meaning as use, and its relation to naming, in order to see what it is.

On Wittgenstein’s view, the meaning of a term is its use in the language of which it is a part (PI section 43, pp. 20-21). It must be noted that Wittgenstein is not asserting the rather trivial thesis that a term—if one could even call it a term—would not be meaningful if no one ever spoke it or wrote it down or in any way employed it in communication. Nor is he maintaining the equally trivial thesis that a term’s meaning depends on the particular way it is used, so that it would have meant something different if it had been used differently. These theses are true of course, but Wittgenstein is making the far stronger claim that the meaning of a term consists in the way it is used to shape behavior, and in its role or utility in our lives.

Wittgenstein distinguishes the meaning of a name from the bearer of a name. (See PI sections 39-44, pp. 19-21.) The bearer of a name is the individual to whom it refers, while the meaning of a name is the set of rules which determine whether or not a name has been correctly applied to this individual. Wittgenstein thinks that the bearers of proper names have little to do with their names’ meaning because a proper name can be meaningful even when its bearer has ceased to exist. According to Wittgenstein, naming is preparatory for actual use. Names can refer to things, but they can do so only in the context of a language game: “Naming is so far not a move in the language-game—any more than putting a piece in its place on the board is a move in chess. We may say: nothing has so far been done, when a thing has been named. It has not even got a name except in the language game.” (PI section 49, p. 24) For Wittgenstein, then, naming—and hence reference—play but a minor role in the mechanics of language.

Given the account of meaning and reference sketched above, it is easy to understand why Wittgenstein, in attacking the notion of a private language, focuses his arguments on the notion of a “private ostensive definition”—on how the connection between the private linguist’s sign and the private linguist’s sensation is set up. In section 244 of PI Wittgenstein asks, “How do words refer to sensations?—There doesn't seem to be any problem here; don't we talk about sensations every day, and give them names? But how is the connexion between the name and the thing named set up? This question is the same as: how does a human being learn the meaning of the names of sensations?—of the word “pain” for example.” (PI p. 89) Notice that Wittgenstein here identifies the question of how sensation words come to refer with that of how one learns their meaning. It is this identification—a conflation, in my view—which vitiates the Private Language Argument. To see why, we must contrast Wittgenstein’s view of naming with that of Saul Kripke in Naming and Necessity.